An exact model based dynamic contact angle algorithm

•Typical contact angle algorithms for inclined plane are systematically compared.•Simplified model-based algorithms introduce significant error in some cases.•Bond number can be rapidly and accurately predicted by determined parameter.•Drop apex can be accurately evaluated by ellipse fitting algorithm.•Exact model-based algorithm can accurately get contact angle within whole range. It is hard to accurately evaluate advancing and receding contact angles for drop on inclined surface. Different from existing simplified model-based algorithms, an exact model-based dynamic contact angle algorithm is proposed. A large number of drop profiles on inclined surface with contact angle, inclination angle and Bond number within the nearly whole application range are numerically generated. After systematic investigations, the parameter closely related to Bond number is determined and the Bond number can be predicted relatively accurately and rapid. Thereafter, the Bond number is adjusted according to the dichotomy and the influence of Bond number on drop shape. The methods for determination of drop apex and scale factor of image are presented. By combining the aforementioned methods the exact model-based dynamic contact angle algorithm for drop on inclined surface is proposed. The extensively used dynamic contact angle algorithms and the proposed algorithm are used to hydrophobicity measurement for real drop image and numerical drop profile on inclined surface. The results reveal that: only the proposed algorithm can accurately evaluate dynamic contact angle without any limitation on contact angle, drop volume and inclination angle, and at the same time the exact fitted edge can be presented.